A second on esh_ga's recommendation. It's called a "plant prop" by at least two manufacturers (Bond/Garden Zone). Even the least expensive 18" versions do a great job supporting Maximilian sunflower, hibiscus moscheutos, and our other wind/squirrel rocked plants.

Main difference between the Bond and GZ products is that the Bond props include an extra bend to further help keep the stem in the ring - though the GZ varieties have worked fine for us without this.

You can also use pea sticks, branches from trees and shrubs. If they are tall enough and have a fork, cut them to size, stick the thicker end in the ground near the base of your plant. The forked part will hold the flowering stalk. More than one support may be necessary for heavy stalks

River birch produces lots of great support sticks which naturally shed in spring. You can use them to support your plants. If you cut back any shrubs, save the branches.

Once you have placed the stick in the ground, cut off excess twigs that are too long. Use a few supports . This is the most discreet and natural way to keep your plants upright.

New thriving plant in pot, grown from seed.
Long before any petals, leafless vertical extension of leafed stem grows tall,
and weight of flower bud bends stem straight down.
The resultant small kink leads to death of stem,
despite subsequent good support and restriction of movement.

Yes, one might support /restrict in advance (much work for many flower stems).
But I do not even know the likelihood of recurrence,
and I am writing to ask you Echinacea-experienced readers about that.

Nice photo, Carol. I always use sticks when I put in a tall transplant. However, some of my asters and sunflowers got so tall last year that I decided to buy some supports...will put them out in March. The supports are huge, but the plants were about eight feet tall and loaded with blooms this past fall...need something strong. I will try to post a photo this year, actually, two: one before the plants grow up through the support, and one after.

Four,
It sounds like your seedling may not be getting enough light, so it grows tall and spindly in an effort to find light. Another method to try is to have a small fan blowing near your seedlings as soon as they've germinated. The breeze from the fan will cause the stems to grow stiffer in an effort to combat the swaying effect of the fan. Result, hopefully, is stronger stems and less drooping. Ideally, get those seedlings outside ASAP where they experience true wind and strong sunlight as they grow.

Four,
Is your plant one of the newer developed species or hybrids? It may have been bred to have bigger blooms than the stems can support. Especially if the same thing is happening to every stem. I've grown lots of coneflowers and never had your diffulty. Sorry for you struggles.

Stem appearnce is as I see in photos.
Some stems are nearing length of failed first one.
I supported them because I would like to see that
the plant will make flowers, not just buds.
Later I can experiment by leaving future stems unsupported.

One failed, as the bud stems have been doing; it will die.
Sturdy stem (except in the spot of failure, which in this case was closer to flower) added evidence to what I had been thinking, which is
that stem faillures cause the kinks, rather than vice-versa.

Are you sure you aren't out of the natural range for Echinacea? If yours never freeze down then they are continually growing and are going to fall over eventually. Isn't a flower bud on March 1st a little strange?
Maybe the genetics of your particular plant came from the northern end of its range and it thinks its July.